A096743 Numerator of a(n)/2^A005187(n-1), the n-th row sums of A096651^(3/2), with a(0)=1.

1, 1, 5, 35, 135, 1755, 6303, 39815, 132675, 3322515, 10561455, 64566253, 199681945, 2391238415, 7233344915

Offset

0,3

Comments

The denominators are 2^A005187(n-1) (for n>0), where A005187(n) is the number of 1's in binary expansion of 2n. Can the row sums of A096651^(3/2) be said to define the (3/2)-dimensional partitions of n?

Links

Table of n, a(n) for n=0..14.

Formula

a(n)/2^A005187(n-1) = Sum_{k=0..n} A096651(n, k)*A096742(k)/2^A005187(k-1).

Example

Sequence begins: {1,1,5/2,35/8,135/16,1755/128,6303/256,...}.
Formed from the row sums of triangular matrix A096651^(3/2), which begins:
{1},
{0,1},
{0,3/2,1},
{0,15/8,3/2,1},
{0,41/16,27/8,3/2,1},
{0,387/128,53/16,39/8,3/2,1},
{0,1017/256,987/128,65/16,51/8,3/2,1},
{0,4715/1024,753/256,2067/128,77/16,63/8,3/2,1},
{0,11917/2048,29983/1024,-4503/256,3819/128,89/16,75/8,3/2,1},...
The denominator of each element at column n, row k, is A005187(n-k).

Crossrefs

Cf. A096651, A096742, A005187.

Sequence in context: A111877 A179337 A053126 * A026697 A000910 A005562

Adjacent sequences: A096740 A096741 A096742 * A096744 A096745 A096746

Keyword

more,nonn

Author

Paul D. Hanna, Jul 06 2004

Status

approved